# Scalable Polar Code Construction for Successive Cancellation List Decoding: A Graph Neural Network-Based Approach

arXiv: https://arxiv.org/abs/2207.01105 · HTML: https://mlsanity.com/paper/2207.01105/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 3 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Deep Learning-based Polar Code Design](https://mlsanity.com/paper/1909.12035/) (2019)
- [Construction of Polar Codes with Reinforcement Learning](https://mlsanity.com/paper/2009.09277/) (2020)
- [Decoder-tailored Polar Code Design Using the Genetic Algorithm](https://mlsanity.com/paper/1901.10464/) (2019)
- [Reinforcement Learning for Nested Polar Code Construction](https://mlsanity.com/paper/1904.07511/) (2019)

## Built on by (most cited first, 2 of 2)

- [Graph Neural Networks for Channel Decoding](https://mlsanity.com/paper/2207.14742/) (2022)
- [A Reinforcement Learning Based Universal Sequence Design for Polar Codes](https://mlsanity.com/paper/2601.20118/) (2026)

## Abstract (arXiv)

While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit-channels, finding optimal polar codes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL) decoding in an efficient and scalable manner still awaits investigation. This paper first maps a polar code to a unique heterogeneous graph called the polar-code-construction message-passing (PCCMP) graph. Next, a heterogeneous graph-neural-network-based iterative message-passing (IMP) algorithm is proposed which aims to find a PCCMP graph that corresponds to the polar code with minimum frame error rate under CA-SCL decoding. This new IMP algorithm's major advantage lies in its scalability power. That is, the model complexity is independent of the blocklength and code rate, and a trained IMP model over a short polar code can be readily applied to a long polar code's construction. Numerical experiments show that IMP-based polar-code constructions outperform classical constructions under CA-SCL decoding. In addition, when an IMP model trained on a length-128 polar code directly applies to the construction of polar codes with different code rates and blocklengths, simulations show that these polar code constructions deliver comparable performance to the 5G polar codes.